Evolutionary anthropologists and archaeologists have been considerably successful in modelling the cumulative evolution of culture, of technological skills and knowledge in particular. Recently, one of these models has been introduced in the philosophy of science by De Cruz and De Smedt (Philos Stud 157:411–429, 2012), in an attempt to demonstrate that scientists may collectively come to hold more truth-approximating beliefs, despite the cognitive biases which they individually are known to be subject to. Here we identify a major shortcoming in that attempt: De Cruz & De Smedt’s mathematical model makes one particularly strong tractability assumption that causes the model to largely miss its target (namely, truth accumulation in science), and that moreover conflicts with empirical observations. The second, more constructive part of the paper presents an alternative, agent-based model, which allows one to much better examine the conditions for scientific progress and decline.